Henri & Renaud Lifchitz's PRP Top records

What is a PRP ?

A PRP is a probable prime number, a number that nobody knows how to prove or disprove its primality.
Here are some criterions that can be used to recognize these numbers :

- N does not have any prime factor up to 2^32.
- N cannot be trivially written into a product.
- Take 3 square-free consecutive bases such that (b1/N)=(b2/N)=(b3/N)= -1. N should be such that b1^((N-1)/2)=b2^((N-1)/2)=b3^((N-1)/2)= -1 (mod N).
- Take a prime base such that (b/N)= -1 and b<>b1<>b2<>b3. N should pass the strong test in base b.
- or more (if someone has got an idea) !!!

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1-250	251-500	501-750	751-1000	1001-1250	1251-1500	1501-1750	1751-2000
2001-2250	2251-2500	2501-2750	2751-3000	3001-3250	3251-3500	3501-3750	3751-4000
4001-4250	4251-4500	4501-4750	4751-5000	5001-5250	5251-5500	5501-5750	5751-6000
6001-6250	6251-6500	6501-6750	6751-7000	7001-7250	7251-7500	7501-7750	7751-8000
8001-8250	8251-8500	8501-8750	8751-9000	9001-9250	9251-9500	9501-9750	9751-10000

Rank	Probable prime	Digits (> 30000)	Who ?	When ?
9001	6^70974-137	55229	Lelio R Paula	10/2012
9002	2^183446-113073	55223	Enzo Doria	07/2014
9003	2^183441+577294575	55222	Lelio R Paula	03/2013
9004	5^79000-6	55219	Lelio R Paula	10/2012
9005	2^183413-901	55213	Yves Minet	01/2012
9006	19^43168-50	55202	Lelio R Paula	02/2013
9007	2^183340+19683	55191	Lelio R Paula	02/2012
9008	6^70923+35	55189	Lelio R Paula	10/2012
9009	2^183317-4035	55184	Lelio R Paula	01/2011
9010	2^183284-15	55174	Lelio R Paula	03/2011
9011	2^183255+149	55166	Lelio R Paula	02/2011
9012	4*10^55165+87	55166	Robert Price	05/2016
9013	(3^115574+4)/63037	55139	Lelio R Paula	03/2012
9014	2^183165-112333	55139	Enzo Doria	06/2014
9015	(109^27061-1)/108	55133	Richard Fischer	09/2017
9016	2^183142+855	55132	Lelio R Paula	01/2011
9017	(49*10^55129+383)/9	55130	Robert Price	04/2017
9018	2^183019+255255	55095	Lelio R Paula	01/2011
9019	(10^55084-19)/9	55084	Robert Price	10/2017
9020	3*10^55077+7	55078	Erik Branger	11/2013
9021	(62*10^55075-71)/9	55076	Robert Price	09/2015
9022	27499!2-32	55070	Robert Price	10/2015
9023	15307^3958+3958^15307	55067	Hans Havermann	08/2016
9024	70^29836-69	55051	Norbert Schneider	10/2012
9025	18^43854-83	55049	Lelio R Paula	02/2013
9026	7^65126+58	55038	Lelio R Paula	10/2012
9027	2^182827-1615	55037	Lelio R Paula	11/2009
9028	7*10^55030-9	55031	Dmitry Domanov	11/2010
9029	2^182768-4055	55019	Yves Minet	02/2018
9030	6^70702+23	55017	Lelio R Paula	10/2012
9031	(23*2^182753+1)/151	55014	Lelio R Paula	07/2012
9032	2^182743-1615	55012	Lelio R Paula	11/2009
9033	(24737*2^182736+1)/399	55011	Lelio R Paula	05/2014
9034	3^115280-9568	55003	Enzo Doria	02/2013
9035	2^182656-12849	54985	Enzo Doria	10/2012
9036	12791^13388-13388^12791	54984	Norbert Schneider	03/2018
9037	9*19^42995+16	54981	Curtis Bright	05/2015
9038	2^182627+28425	54977	Lelio R Paula	11/2009
9039	2^182597-113053	54968	Enzo Doria	07/2014
9040	(3^115213+2)/30906725	54964	Lelio R Paula	03/2012
9041	2^182581-1975	54963	Yves Minet	09/2012
9042	(2*10^54960-179)/3	54960	Robert Price	11/2017
9044	27449!!-16	54959	Robert Price	06/2015
9043	(22*10^54958-73)/3	54959	Robert Price	09/2017
9046	4^91283-3^91283	54958	Jean-Louis Charton	01/2004
9045	2^182565+107	54958	Lelio R Paula	11/2009
9047	2^182560+2053	54957	Lelio R Paula	12/2010
9048	2^182451-182451	54924	Henri Lifchitz	10/2004
9049	2^182444+81	54922	Henri Lifchitz	10/2005
9050	2^182433+74105	54918	Enzo Doria	04/2016
9051	20^42206-5243	54912	Enzo Doria	03/2013
9052	2^182394+85	54907	Lelio R Paula	02/2011
9053	2^182374-112287	54901	Enzo Doria	06/2014
9054	(47^32833-33^32833)/14	54899	Serge Batalov	12/2016
9055	2^182363-113167	54897	Enzo Doria	07/2014
9056	2^182359-112221	54896	Enzo Doria	06/2014
9057	(F(1905)^139-F(1904)^139)/F(1903)	54893	Wayne Halsdorf	05/2010
9058	(17*2^182274+1)/1467	54869	Lelio R Paula	01/2012
9059	18^43698-5	54853	Lelio R Paula	02/2013
9060	2^182209-1893	54851	Yves Minet	09/2012
9061	2^182194-3443	54846	Yves Minet	12/2016
9062	15023^4468+4468^15023	54836	Hans Havermann	08/2016
9063	2^182135+90143	54829	Yves Minet	10/2010
9064	2^182119+74333	54824	Enzo Doria	04/2016
9065	14289^6860+6860^14289	54818	Hans Havermann	08/2016
9066	3^114892-114892^3	54818	Norbert Schneider	03/2017
9067	2^182070-47355	54809	Lelio R Paula	01/2011
9068	3^114869+76	54807	Lelio R Paula	10/2012
9069	8^60681-60681^8	54801	Norbert Schneider	12/2016
9070	1897^16710+16710^1897	54777	Serge Batalov	05/2014
9071	Phi(61868,59)	54776	Enzo Doria	04/2012
9072	113^26679+2	54775	Lelio R Paula	05/2013
9073	3^114789-74	54769	Lelio R Paula	10/2012
9074	15^46567+98	54768	Lelio R Paula	02/2013
9075	(2*10^54767-71)/3	54767	Robert Price	01/2017
9076	(298*10^54765-7)/3	54767	Robert Price	06/2017
9077	(21*2^181931-1)/169997	54763	Lelio R Paula	01/2014
9078	2^181913+29	54762	Henri Lifchitz	06/2005
9079	(31*10^54761-121)/9	54762	Robert Price	06/2016
9080	2^181887+189	54754	Lelio R Paula	02/2011
9081	2^181874+181874^2-1	54750	Robert Price	04/2014
9082	(2^181865+9)/7339	54743	Lelio R Paula	02/2012
9083	5^78314-92	54740	Lelio R Paula	10/2012
9084	(163*10^54727-1)/9	54729	Serge Batalov	12/2014
9085	15^46531+74	54725	Lelio R Paula	02/2013
9086	277^22400-348	54712	Enzo Doria	07/2012
9087	6^70302+101	54706	Lelio R Paula	10/2012
9088	3^114622-10408	54689	Enzo Doria	02/2013
9090	(23*2^181674+1)/489	54688	Lelio R Paula	01/2012
9089	2^181669-1551	54688	Yves Minet	08/2012
9091	(57352^11491-1)/57351	54676	Serge Batalov	04/2015
9092	(31*2^181629-1)/10734721	54671	Lelio R Paula	01/2014
9093	(F(1048)^251-F(1047)^251)/F(1046)	54668	Wayne Halsdorf	05/2010
9094	13^49073+46	54665	Lelio R Paula	01/2013
9095	(57042^11491-1)/57041	54649	Serge Batalov	04/2015
9097	20^42000+73	54644	Lelio R Paula	02/2013
9096	(67607*2^181517+1)/1655	54644	Lelio R Paula	05/2014
9098	33*10^54634+7	54636	Robert Price	07/2016
9099	20^41988+61	54628	Lelio R Paula	01/2013
9100	20^41988-8123	54628	Enzo Doria	03/2013
9101	2^181420+21181	54613	Yves Minet	03/2011
9102	(19*10^54608+161)/9	54609	Robert Price	07/2016
9103	19^42696-24	54598	Lelio R Paula	02/2013
9104	(44*10^54596-503)/9	54597	Robert Price	10/2017
9105	(74*10^54583+61)/9	54584	Robert Price	10/2015
9106	2^181316-94395	54582	Lelio R Paula	09/2011
9107	14751^5006+5006^14751	54572	Hans Havermann	08/2016
9108	14^47609+39	54567	Lelio R Paula	02/2013
9109	12696^13295-13295^12696	54559	Norbert Schneider	01/2018
9110	(2^124979+lucasV(2,-2,124979)+1)/3	54552	Paul Vanderveen	12/2017
9112	3^114327-74	54548	Lelio R Paula	10/2012
9111	(44*10^54547-161)/9	54548	Robert Price	11/2017
9113	gcd(V(995625),5F(199125)(F(199125)-1)+1)	54546	Serge Batalov	04/2015
9114	(17*10^54537-47)/3	54538	Robert Price	05/2017
9115	2^181155-1155*181155	54534	Henri Lifchitz	02/2005
9116	Phi(61672,83)	54533	Enzo Doria	05/2012
9117	(2*10^54527-197)/3	54527	Robert Price	11/2017
9118	9*2^181128+7	54526	Lelio R Paula	03/2014
9119	89*10^54518-7	54520	Robert Price	03/2017
9120	2^181090-113247	54514	Enzo Doria	07/2014
9121	14031^7670+7670^14031	54508	Hans Havermann	08/2016
9122	14210^6849+6849^14210	54505	Hans Havermann	08/2016
9123	2^181043-199	54500	Lelio R Paula	02/2011
9124	12^50499+5	54498	Lelio R Paula	01/2013
9125	12^50491+5	54489	Lelio R Paula	01/2013
9126	6^70016-145	54484	Lelio R Paula	10/2012
9127	11^52313-9600	54479	Enzo Doria	02/2013
9128	2^64459+3^64459+5^64459+7^64459	54475	Henri Lifchitz	08/2001
9129	2^180946-111041	54471	Enzo Doria	05/2014
9130	(64*10^54467+287)/9	54468	Robert Price	04/2016
9131	(32*10^54458+319)/9	54459	Robert Price	10/2017
9132	5^77907-2*3^77907	54455	Mike Oakes	11/2009
9133	20^41853-5623	54453	Enzo Doria	03/2013
9134	14^47506-75	54448	Lelio R Paula	02/2013
9135	(25*10^54443-67)/3	54444	Robert Price	11/2017
9136	2^180839-113437	54438	Enzo Doria	08/2014
9137	3^114085+28	54433	Lelio R Paula	10/2012
9138	Phi(141230,10)	54432	Ray Chandler	08/2009
9139	6^69946-55	54429	Lelio R Paula	10/2012
9140	p(11796)#/2-1024	54427	Robert Price	09/2017
9141	5*2^180796+3	54426	Lelio R Paula	03/2014
9142	(23*2^180782-1)/91	54421	Lelio R Paula	01/2014
9143	9*6^69928-7	54416	Lelio R Paula	09/2014
9144	92^27701-91^27701	54399	Robert Price	08/2015
9145	(2^180687-3)*6-7	54393	Gilbert Mozzo	04/2016
9146	(5*10^54388-11)/3	54389	Erik Branger	12/2013
9147	20^41799-3043	54382	Enzo Doria	03/2013
9148	13860^8387+8387^13860	54382	Hans Havermann	08/2016
9149	(F(19)^15017-F(18)^15017)/F(17)	54378	Wayne Halsdorf	05/2010
9150	7^64329-18	54365	Lelio R Paula	10/2012
9151	2^180551-967	54352	Yves Minet	01/2012
9152	15^46209-74	54347	Lelio R Paula	02/2013
9153	10^54345+29739	54346	Patrick De Geest	08/2013
9154	10^54345-141381	54345	Patrick De Geest	09/2013
9155	lucasU(2098,1,16360)-lucasU(2098,1,16359)	54342	Mike Oakes	05/2009
9156	177^24171-2	54336	Lelio R Paula	10/2017
9157	2^180496+15	54335	Lelio R Paula	02/2011
9158	1845^16636+16636^1845	54334	Serge Batalov	05/2014
9159	11^52169-70	54329	Lelio R Paula	01/2013
9160	2^180446-4031	54320	Yves Minet	02/2018
9161	13693^9262+9262^13693	54317	Hans Havermann	06/2016
9162	2^180429-113101	54315	Enzo Doria	07/2014
9163	2^180423-112051	54313	Enzo Doria	05/2014
9164	16112^2349+2349^16112	54312	Hans Havermann	06/2016
9165	(79^28621-1)/78	54311	Paul Bourdelais	08/2017
9166	(13^48751+4^48751)/17	54305	Robert Price	05/2013
9167	2^180370+12915	54297	Lelio R Paula	09/2012
9168	(10^54290+41)/3	54290	Robert Price	01/2017
9169	15108^3917+3917^15108	54283	Hans Havermann	06/2016
9170	2^180317-3019	54281	Yves Minet	10/2014
9171	2^180314+855	54280	Lelio R Paula	10/2009
9172	19^42425+94	54252	Lelio R Paula	02/2013
9173	2^180180-1005449	54240	Paul Bourdelais	11/2012
9174	2^180173-2773	54238	Yves Minet	07/2014
9175	13367^11418+11418^13367	54238	Hans Havermann	06/2016
9176	427^20614+20614^427	54224	Norbert Schneider	06/2016
9177	2^180124-87959	54223	Gary Barnes	08/2009
9178	2^180111-113101	54219	Enzo Doria	07/2014
9179	2^180101-114871	54216	Enzo Doria	05/2015
9180	(11*2^180099+1)/51617	54212	Lelio R Paula	07/2012
9182	2^180070+465	54207	Lelio R Paula	09/2012
9181	13683^9154+9154^13683	54207	Hans Havermann	06/2016
9183	8105225132^180009-95312^9531-1	54198	Jiong Sun	12/2003
9184	2^180014+613	54190	Jason Earls	04/2008
9185	2^180007+101	54188	Lelio R Paula	02/2011
9186	2^180001+41877	54186	Jim Fougeron	08/2002
9187	2^180000+130153	54186	Jim Fougeron	09/2002
9188	3^113565-74	54185	Lelio R Paula	10/2012
9189	50^31891-49	54182	Norbert Schneider	07/2014
9190	(5*2^179991-1)/11427	54180	Lelio R Paula	01/2014
9191	3^113548+26	54177	Lelio R Paula	10/2012
9192	(lucasV(1,2,360029)-2)/(3^3522251725981)	54177	Mike Oakes	04/2017
9193	181^23996-2	54176	Lelio R Paula	10/2017
9194	4159^14969-138	54173	Enzo Doria	07/2012
9196	2^179955+5775	54172	Lelio R Paula	10/2009
9195	2^179953-231313	54172	Enzo Doria	05/2014
9197	5^77485+6	54160	Lelio R Paula	10/2012
9198	18^43141+85	54154	Lelio R Paula	02/2013
9199	10^54149+187647	54150	Patrick De Geest	07/2017
9202	3^113489-340	54149	Lelio R Paula	10/2012
9200	10^54149-800001	54149	Robert Price	06/2017
9201	10^54149-36501	54149	Patrick De Geest	07/2017
9203	7^64070+90	54146	Lelio R Paula	10/2012
9204	12549^13210-13210^12549	54143	Norbert Schneider	12/2017
9205	18^43131+71	54142	Lelio R Paula	02/2013
9206	2^179826-131	54134	Lelio R Paula	02/2011
9207	2^179815-112735	54130	Enzo Doria	06/2014
9208	2^179806+73849	54127	Enzo Doria	04/2016
9209	2^179790+33	54123	Donovan Johnson	02/2006
9210	14287^6138+6138^14287	54120	Hans Havermann	06/2016
9211	(17*10^54117+1)/9	54118	Serge Batalov	05/2010
9212	2^179763-189	54115	Lelio R Paula	02/2011
9213	(21181*2^179770+1)/3029105	54115	Lelio R Paula	05/2014
9214	1828^16589+16589^1828	54113	Serge Batalov	05/2014
9216	20^41588-5883	54108	Enzo Doria	03/2013
9215	50^31847-49	54108	Norbert Schneider	07/2014
9217	2^179733-6855	54106	Lelio R Paula	10/2009
9218	20^41584-5583	54103	Enzo Doria	03/2013
9219	10^54084+3*3^54084	54085	Mike Oakes	05/2010
9220	2^179613-1795	54069	Lelio R Paula	10/2009
9221	2^179589-1011523	54062	Paul Bourdelais	11/2012
9222	2^179574-2531	54058	Yves Minet	07/2014
9223	(41*10^54051-23)/9	54052	Robert Price	05/2015
9224	117^26131-116	54044	Norbert Schneider	10/2013
9225	(10^54038-31)/3	54038	Serge Batalov	12/2014
9226	11^51885-84	54033	Lelio R Paula	01/2013
9227	14990^4011+4011^14990	54013	Hans Havermann	07/2016
9228	(19*2^179414+1)/7	54010	Lelio R Paula	07/2012
9229	3^113182-10408	54002	Enzo Doria	02/2013
9230	35^34970-8786	53997	Enzo Doria	03/2013
9231	2^179371-1637587	53997	Enzo Doria	05/2015
9232	19^42225-92	53996	Lelio R Paula	01/2013
9233	10190^13471-13471^10190	53995	Norbert Schneider	05/2018
9234	(3^113188+7)/73917675784	53994	Lelio R Paula	03/2012
9235	7*3^113162+8	53993	Lelio R Paula	03/2014
9236	(10^53991+179)/9	53991	Serge Batalov	12/2014
9238	2^179350-2145	53990	Lelio R Paula	10/2009
9237	(-lucasV(1,2,358718)-2)/(51719)	53990	Mike Oakes	04/2017
9239	8^59782-6^59782-3^59782	53989	Mike Oakes	11/2009
9240	3*7^63861+8	53970	Lelio R Paula	09/2014
9241	2^179274+71389	53967	Enzo Doria	04/2016
9242	2^179259-58695	53963	Lelio R Paula	10/2009
9243	6^69345+61	53961	Lelio R Paula	10/2012
9244	(-lucasV(1,2,358635)+2)/(71793172321719602511716271)	53957	Mike Oakes	04/2017
9245	(40216^11719-1)/40215	53955	Serge Batalov	04/2015
9246	89*10^53951-9	53953	Robert Price	05/2017
9247	14^47067-3	53945	Lelio R Paula	01/2013
9248	p(11700)#/2-512	53937	Robert Price	07/2017
9249	(2^179168-5)/59	53934	Lelio R Paula	02/2012
9250	2^179128+8415	53923	Lelio R Paula	07/2012

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Probable Primes Top 10000

(218736 PRPs in the top)